Le 22/03/2014 19:13, Nathaniel Smith a écrit :
Hi all,
After 88 emails we don't have a conclusion in the other thread (see [1] for background). But we have to come to some conclusion or another if we want @ to exist :-). So I'll summarize where the discussion stands and let's see if we can find some way to resolve this.
The fundamental question is whether a chain like (a @ b @ c) should be evaluated left-to-right (left-associativity) or right-to-left (right-associativity).
DATA SOURCE 1:
This isn't a democratic vote, but it's useful to get a sense of people's intuitions. Counting messages in the other thread, opinion seems to be pretty evenly split:
== "Votes" for right-associativity == Weak-right: [2] [3] [5] Tight-right: [4] [6] Same-right: [11]
== "Votes" for left-associativity == Same-left: [7] [8] [14] [15] [16] Tight-left: [9] Weak-left: [12]
There's also the "grouping" option (described in [10]), but that's received very little support (just [13]).
DATA SOURCE 2:
Several people have suggested that performance considerations mean that right-to-left evaluation is more common in practice than left-to-right evaluation. But, if we look at actual usage in Python code, that's not what we find: when people call dot() in chains, then they're about evenly split, and actually use the left-to-right, left-associative order slightly more often than the right-to-left, right-associative order: http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069578.html
DATA SOURCE 3:
And if we look at other languages, then we find:
== "Votes" for right-associativity == <none>
== "Votes" for left-associativity == Same-left: Matlab, Julia, IDL, GAUSS Tight-left: R
This is a very strong point. Lots of people come to python with a background and would be surprised if python behaves differently than other mainstream frameworks. I'll add that simpler is better, multiplications should behave the same way, and vote for same-left.
And Mathematica uses the "grouping" approach.
ARGUMENTS:
The final outcome of this is that I need to write a piece of text that says what our (at least rough) consensus is, and lays out the reasons. So long as the "vote" is so evenly split, I can't really do this. But I can imagine what the different pieces of text might look like.
THE CASE FOR LEFT-ASSOCIATIVITY:
If I were writing this text in favor of left-associativity, I'd point out:
- "Special cases aren't special enough to break the rules". Every single operator in Python besides ** is left-associative (and ** has very compelling arguments for right associativity). @ does not have similarly compelling arguments. If we were having this debate about "*", then it'd probably be much more lopsided towards left-associativity. So sure, there's something about @ that makes right-associativity *more* appealing than for most other operators. But not *much* more appealing -- left-associativity still comes out at least slightly ahead in all of the above measures. And there are a lot of benefits to avoiding special cases -- it gives fewer rules to memorize, fewer rules to remember, etc. So @ may be a special case, but it's not special enough.
- Other languages with @ operators almost overwhelmingly use the "same-left" rule, and I've never heard anyone complain about this, so clearly nothing horrible will happen if we go this way. We have no comparable experience for right-associativity.
- Given left-associativity, then there's good agreement about the appropriate precedence. If we choose right-associativity then it's much less clear (which will then make things harder for experts to remember, harder for non-experts to guess, etc.). Note that one of the votes for right-associativity even preferred the "same-right" rule, which is not even technically possible...
This strikes me as a nice solid case.
THE CASE FOR RIGHT-ASSOCIATIVITY:
If I were writing this text in favor of right-associativity, I'd point out:
- Because matrix multiplication has a tight conceptual association with function application/composition, many mathematically sophisticated users have an intuition that a matrix expression like R S x proceeds from right-to-left, with first S transforming x, and then R transforming the result. This isn't universally agreed, but at the least this intuition is more common than for other operations like 2 * 3 * 4 that everyone reads as going from left-to-right.
- There might be some speed argument, if people often write things like "Mat @ Mat @ vec"? But no-one has found any evidence that people actually do write such things often.
- There's been discussion of how right-associativity might maybe perhaps be nice for non-matmul applications? But I can't use those arguments [17] [18].
- ...... I got nothin'.
I am fine with any outcome here. (I'm actually listed under *both* tight-right and same-left in the straw poll above ;-).) I'm totally happy to go back to Guido et al and argue for right-associativity. BUT if you all want me to do that then you need to give me some better arguments to use :-).
One way to do this might be to go through the ((a @ b) @ c) and (a @ (b @ c)) examples I found (the scripts are available [19], and I can help modify them to spit out more details), look at the actual code, and demonstrate that the left-to-right ((a @ b) @ c) cases are mostly ones where evaluation order doesn't matter (i.e., they could have just as well been written the other way), and the right-to-left (a @ (b @ c)) ones are ones where right-to-left really is better than left-to-right. I have no idea if this is true, and it'll require some reading of the surrounding code to figure out what the matrix shapes are, but if it *is* true then at least that'd be something solid that right-associativity advocates could point to.
WHAT NOW:
If seeing this summary laid out caused you to change your mind one way or the other, then please reply and say so!
If you think of some way to get more data that could favor one or the other option (running some kind of usability experiment on people? [20]), then please share!
If you think of some other arguments in favor of left-associativity, then please share!
If you think of some other arguments in favor of right-associativity, especially ones that are based on something besides your gut feeling, then PLEASE PLEASE share!
Thanks, -n
[1] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069444.html [2] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069446.html [3] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069450.html [4] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069452.html [5] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069455.html [6] https://mail.python.org/pipermail/python-ideas/2014-March/027124.html [7] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069512.html [8] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069513.html [9] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069467.html [10] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069530.html [11] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069537.html [12] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069540.html [13] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069571.html [14] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069514.html [15] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069531.html [16] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069567.html [17] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069527.html [18] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069584.html [19] https://gist.github.com/njsmith/9157645 [20] http://mail.scipy.org/pipermail/numpy-discussion/2014-March/069584.html
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